3x^2-150x=10000

Solution for 3x^2-150x=10000 equation:

3x^2-150x=10000

We move all terms to the left:

3x^2-150x-(10000)=0

a = 3; b = -150; c = -10000;
Δ = b2-4ac
Δ = -1502-4·3·(-10000)
Δ = 142500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{142500}=\sqrt{2500*57}=\sqrt{2500}*\sqrt{57}=50\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-50\sqrt{57}}{2*3}=\frac{150-50\sqrt{57}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+50\sqrt{57}}{2*3}=\frac{150+50\sqrt{57}}{6}
$